How Window Air Conditioner Works

Lee is a new student at the University of Oklahoma. He rents a small apartment which has a window air conditioner in his bedroom (small room). Lee spends most of his time at school, hence he only wants to run the air conditioner when he is at home. But he worries that it will take too long for the room temperature to reach the disred level. Also, he is interested in knowing how much heat will be released to the outside ambient air during the cooling process.

What is known:

• Coefficient of performance, COP, (the ratio of the heat removed from the room to the net work required for the air conditioner) of the air conditioner COP = 2.5
• Power input of the air conditioner
       dW/dt = = 900 W
• Room temperature T_room = 90^oF
• Temperature setting of the air conditioner,
  T_setting = 75 ^oF
• 50 kJ heat needs to be removed for the temperature of the room to go down 1^o F

• How long time will it take to cool the room down to the temperature setting?
• How much heat will be released to the ambient?

• Take the window air conditioner as a system
• The energy balance equation is:
  (Q_in - Q_out ) + (W_in - W_out)
         + (E_mass,in - E_mass,out) = ΔE_system